26
speed of 1 m/s. Later chapters will discuss the force concept in more detail.
In fact, this entire book is about the relationship between force and motion.
In the previous section, I gave a gravitational definition of mass, but by
defining a numerical scale of force, we can also turn around and define a
scale of mass without reference to gravity. For instance, if a force of two
Newtons is required to accelerate a certain object from rest to 1 m/s in 1 s,
then that object must have a mass of 2 kg. From this point of view, mass
characterizes an object’s resistance to a change in its motion, which we call
inertia or inertial mass. Although there is no fundamental reason why an
object’s resistance to a change in its motion must be related to how strongly
gravity affects it, careful and precise experiments have shown that the
inertial definition and the gravitational definition of mass are highly
consistent for a variety of objects. It therefore doesn’t really matter for any
practical purpose which definition one adopts.
Discussion Question
Spending a long time in weightlessness is unhealthy. One of the most
important negative effects experienced by astronauts is a loss of muscle and
bone mass. Since an ordinary scale won’t work for an astronaut in orbit, what
is a possible way of monitoring this change in mass. (Measuring the
astronaut’s waist or biceps with a measuring tape is not good enough, because
it doesn’t tell anything about bone mass, or about the replacement of muscle
with fat.)
0.7Less Common Metric Prefixes
The following are three metric prefixes which, while less common than
the ones discussed previously, are well worth memorizing.
prefixmeaningexample
mega-M10
6
6.4 Mm= radius of the earth
micro-
µ
10
-6
10
µ
m= size of a white blood cell
nano-n10
-9
0.154 nm= distance between carbon
nuclei in an ethane molecule
Note that the abbreviation for micro is the Greek letter mu,
µ
— a
common mistake is to confuse it with m (milli) or M (mega).
There are other prefixes even less common, used for extremely large and
small quantities. For instance, 1 femtometer=10
-15
m is a convenient unit
of distance in nuclear physics, and 1 gigabyte=10
9
bytes is used for comput-
ers’ hard disks. The international committee that makes decisions about the
SI has recently even added some new prefixes that sound like jokes, e.g. 1
yoctogram = 10
-24
g is about half the mass of a proton. In the immediate
future, however, you’re unlikely to see prefixes like “yocto-” and “zepto-”
used except perhaps in trivia contests at science-fiction conventions or other
geekfests.
10
-9
10
-6
10
-3
10
3
10
6
Nine little
nano
micro
milli
kilo
mega
nuns
mix
milky
mugs.
This is a mnemonic to help you
remember the most important
metric prefixes. The word "little"
is to remind you that the list starts
with the prefixes used for small
quantities and builds upward. The
exponent changes by 3 with each
step, except that of course we do
not need a special prefix for 100,
which equals one.
Chapter 0Introduction and Review